Computational Finite Element Methods in Nanotechnology

Sarhan M. Musa

• Publisher: CRC Press
• Year: 2017
• eBook ISBN: 9781351832595
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Computational Finite Element Methods in Nanotechnology demonstrates the capabilities of finite element methods in nanotechnology for a range of fields. Bringing together contributions from researchers around the world, it covers key concepts as well as cutting-edge research and applications to inspire new developments and future interdisciplinary research. In particular, it emphasizes the importance of finite element methods (FEMs) for computational tools in the development of efficient nanoscale systems.

The book explores a variety of topics, including:

• A novel FE-based thermo-electrical-mechanical-coupled model to study mechanical stress, temperature, and electric fields in nano- and microelectronics
• The integration of distributed element, lumped element, and system-level methods for the design, modeling, and simulation of nano- and micro-electromechanical systems (N/MEMS)
• Challenges in the simulation of nanorobotic systems and macro-dimensions
• The simulation of structures and processes such as dislocations, growth of epitaxial films, and precipitation
• Modeling of self-positioning nanostructures, nanocomposites, and carbon nanotubes and their composites
• Progress in using FEM to analyze the electric field formed in needleless electrospinning
• How molecular dynamic (MD) simulations can be integrated into the FEM
• Applications of finite element analysis in nanomaterials and systems used in medicine, dentistry, biotechnology, and other areas

The book includes numerous examples and case studies, as well as recent applications of microscale and nanoscale modeling systems with FEMs using COMSOL Multiphysics® and MATLAB®. A one-stop reference for professionals, researchers, and students, this is also an accessible introduction to computational FEMs in nanotechnology for those new to the field.

1

Overview of Computational Methods in Nanotechnology

Orion Ciftja

Prairie View A&M University, Prairie View, Texas

Sarhan M. Musa

Prairie View A&M University, Prairie View, Texas

CONTENTS

1.1 Introduction

1.2 Nanoscale Structures Relevant to Nanotechnology

1.3 Modeling Methods

1.3.1 Modeling of Carbon Nanotubes and Nanocomposites

1.3.2 Modeling of Electronic Quantum Dots

1.3.3 Modeling of Quantum Wires and Nano-MOSFET Devices

1.4 Finite Element Method for Capacitance Extraction of Interconnects in Microscale Circuits

1.4.1 Microscale Single Interconnect Line on Si–SiO₂ Substrate

1.4.2 Microscale Coupled Interconnect Lines on Si–SiO₂ Substrate

1.5 Conclusion

Acknowledgment

References

1.1 Introduction

If one considers which research areas in physics, chemistry, and engineering experienced the strongest growth in the last 10 years, then it is likely that material sciences and nanotechnology stand out as front runners. While it is fair to say that material sciences have always been important, it is also true to state that until very recently they were somehow limited in scope. Before the nanotechnology revolution, all material sciences research was basically dominated by physics and engineering. The major driving force behind such research were attempts in computer and information technologies to miniaturize transistors and electronic processors. Essentially, all was a top-down strategy: start with a macroscopic device and then try to make it smaller and smaller.

Nanotechnology introduced an absolute change in this mindset. Namely, the new nanoscale branch of modern material sciences is now more concerned with a bottom-up strategy. Nowadays, one wants to manipulate atoms/molecules in such a way as to form new artificial nanostructures with defined properties either by self-assembly or by self-organization. At present, nanotechnology reaches from nanoelectronics to biomedical applications, and the importance of the field can in no way be underestimated. Nanotechnology offers unlimited possibilities for advancement in many physical and engineering sciences. It also offers unprecedented possibilities for development of novel technologies, as well. A wide variety of nanomaterials are now used in engineering, pharmaceutical, biomedical products, as well as other industries. While nanoscale materials possess more novel and unique physical–chemical properties than bulk materials, they are not easy to study. Therefore, studies of nanomaterials have generated intense scientific curiosity, attracting much attention for the last few years.

Together with the experimental developments in nanotechnology, the fundamental techniques of theory and modeling have seen a revolution that parallels the advances on which the field of nanotechnology is based. The last two decades have seen the development of density functional theory (DFT), classical Monte Carlo (MC) techniques, quantum Monte Carlo (QMC) methods, molecular dynamics (MD) simulations, and fast multigrid algorithms. New insights have come from the application of these and other new theoretical and computational tools. Advances in computing and combination of new theoretical methods with high computer power have made possible the simulation of complex systems with million degrees of freedom.

Advances in nanotechnology have created a more pressing need for a better quantitative understanding of nanoscale systems. Absence of quantitative models and robust computational methods applied to newly observed nanoscale phenomena increasingly limits a quicker progress in the field. The use of the full potential of novel theoretical and modeling tools has the great beneficial effect to seriously accelerate widespread applications in many areas of nanotechnology. Realizing this potential, however, will require long-term fundamental research and expanded educational opportunities to train the next generation of scientists and engineers whose job is to overcome fundamental theoretical and computational challenges in nanotechnology. Although our ability to synthesize and fabricate various nanostructures such as quantum dots, quantum wires, carbon nanotubes, molecular magnets, etc., has constantly improved, we have not reached yet the phase of being able to incorporate them together in larger functional systems or devices.

From a theoretical and modeling perspective, it is not easy to study or model the properties of systems that span the whole range from macroscopic to microscopic length and time scales. It is also not easy to determine the transport mechanisms of various devices at the nanoscale. Studies of nanointerfaces generally are quite difficult, and it is not easy to describe with reasonable accuracy the response of nanoscale structures to external probes such as electric field, magnetic field, radiation, etc. Nevertheless, even though some of the challenges given earlier appear insurmountable, opportunities for research and discovery in nanotechnology outweigh the risks by far and large. New tools and techniques are giving us the ability to put atoms and molecules where we want them. Researchers are discovering new properties that emerge at nanometer length scales that are different from the properties of both individual atoms/molecules and bulk materials. Scientists and engineers have successfully synthesized and characterized a broad range of fundamental nanosystems with potentially useful properties. There is a convergence in length scales between inorganic nanostructures and biomolecules such as DNA and proteins. Nanostructures such as quantum dots are being used as biosensor assays. Overall, these are exciting times for the field of nanotechnology.

Latest nanotechnology developments offer the possibility for revolutionary advances in fundamental sciences and engineering. Nanotechnology raises research issues that are fundamental to a growing number of disciplines and the potential for applications of enormous economic and social significance. The basic theoretical approaches and modeling methods that go on par with such scientific developments have seen a revolution that parallels the experimental advances on which the field of nanotechnology is based. Advances in computing and combination of new theoretical methods with high computer power have shed more light on the properties of various nanoscale systems, but at the same time, these works indicate that current algorithms and numerical methods must be made more efficient and, perhaps, new ones should be invented. Clearly, the nanotechnology revolution has created an urgent need for more robust computational methods to understand the properties of matter at the nanoscale.

In this chapter, we will give a brief overview of some modeling challenges faced in the field of nanoscale research and will describe some of the most important computational methods already in use in various nanotechnology disciplines.

1.2 Nanoscale Structures Relevant to Nanotechnology

In recent years, interest in the area of nanotechnology has exploded worldwide including many institutes, laboratories, and universities where researchers from different disciplines have been working together in many aspects of nanotechnology. Nanotechnology represents a compelling case to bring groups of multidisciplinary scientists to work together on understanding phenomena at the nanoscale. Only this approach will allow us to have a share in the nanotechnology research, create strong educational programs, institute interdisciplinary research areas, spark additional collaborations between scientists, and at the end harvest all the expected benefits. This approach stimulates the formation of alliances and teams of scientists with diverse background to meet the challenge of developing a broad quantitative understanding of structure and dynamics at the nanoscale. Such cohesion between different disciplines is key to sparking additional collaboration across disciplinary boundaries and addressing some critical research issues in this fast-evolving field.

Given the rapid expansion of the field of nanotechnology, it is practically impossible to mention all the nanoscale structures or devices that are currently used or studied. Because of this, in this work, we are not even attempting to give a detailed description. On the contrary, we will focus our attention on few important nanoscale devices that, in our view, are relevant to the field of nanotechnology. We have placed in this category structures such as carbon nanotubes/composites, quantum dots, and quantum wires, just to mention a few. The key idea of our approach is to give a rather brief overview of the properties of such structures and then describe various computational methods used to study their properties. Well-characterized nanoscale elements like the ones mentioned earlier need to be quantitatively understood. Just as knowledge of the atom allows us to make and manipulate larger structures, knowledge of important nanoscale elements will allow us to reliably manufacture larger artificial structures with prescribed properties. Such nanoscale elements will be the centerpiece of new functional nanomechanical, nanoelectronic, and nanomagnetic devices. Thus, a quantitative understanding of the electronic, magnetic, transport, and mechanical properties of key nanoscale elements is crucial to building novel technological devices.

Without a coherent description of some of these key nanoscale elements, overall progress in the field of nanotechnology will be limited. In the following, we focus our attention basically on three groups of nanoscale structures relevant to nanotechnology:

1. Carbon nanotubes and composite systems

2. Electronic quantum dots

3. Quantum wires and nano-metal–oxide–semiconductor field-effect transistor (nano-MOSFET) devices

These important nanoscale structures are well defined by experiment and tractable using standard theoretical and computational tools. Moreover, they have been demonstrated to hold promise in future nanotechnologies. All computational methods devised to study the properties of these nanoscale structures attempt to solve accurately problems such as understanding the response of nano-building blocks and nanodevices to external probes, explore novel theories and models to predict behavior and reliability of nanosensors and devices, understand classical and quantum transport in nanostructures, and so on.

1.3 Modeling Methods

Studies of nanoscale structures offer great promise but require new theoretical approaches and computationally intensive studies. MD simulation methods can handle systems with tens of thousands of atoms; however, to fully exploit their power, algorithms need to be made scalable and fully parallelized. Such methods are especially useful in providing benchmarks for those systems, where experimental data are unreliable or hard to reproduce. Lack of clear prescriptions for obtaining reliable results that apply to nanostructures is another challenging problem for experiment and theory. While new experiments will need to be designed to ensure reproducibility and the validity of the measurements, the theoretical challenge is to construct new theories that would crosscheck such conclusions.

DFT methods with standard exchange functionals are only partially satisfactory when calculating band structures of metals and, especially, semiconductors. Standard DFT fails even totally when describing van der Waals complexes (physisorption) or single-walled carbon nanotubes (SWCNTs), a behavior ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Acknowledgments
• Editor
• Contributors
• 1. Overview of Computational Methods in Nanotechnology
• 2. Finite Element Method for Nanotechnology Applications in Nano-/Microelectronics
• 3. Modeling, Design, and Simulation of N/MEMS by Integrating Finite Element, Lumped Element, and System Level Analyses
• 4. Nanorobotic Applications of the Finite Element Method
• 5. Simulations of Dislocations and Coherent Nanostructures
• 6. Continuum and Atomic-Scale Finite Element Modeling of Multilayer Self-Positioning Nanostructures
• 7. Application of Finite Element Method for the Design of Nanocomposites
• 8. Finite Element Modeling of Carbon Nanotubes and Their Composites
• 9. Finite Element–Aided Electric Field Analysis of Needleless Electrospinning …
• 10. Molecular Dynamic Finite Element Method (MDFEM)
• 11. Application of Biomaterials and Finite Element Analysis (FEA) in Nanomedicine and Nanodentistry
• 12. Application of Finite Element Analysis for Nanobiomedical Study
• 13. Finite Element Method for Micro- and Nano-Systems for Biotechnology
• 14. Design of the Nanoinjection Detectors Using Finite Element Modeling
• 15. Finite Element Method (FEM) for Nanotechnology Application in Engineering: Integrated Use of Macro-, Micro-, and Nano-Systems
• 16. Modeling at the Nano Level: Application to Physical Processes
• Appendix A: Material and Physical Constants
• Appendix B: Symbols and Formulas
• Index